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DOI: 10.1016/j.epsr.2019.106005

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Contents lists available at ScienceDirect

Electric Power Systems Research

journal homepage: www.elsevier.com/locate/epsr

Dynamic characteristics of virtual inertial response provision by DFIG-basedwind turbinesMatej Krpan⁎, Igor KuzleUniversity of Zagreb, Faculty of Electrical Engineering and Computing, 10000 Zagreb, Croatia

A R T I C L E I N F O

Keywords:Wind energy integrationPower system dynamicsWind turbine dynamicsDFIGFrequency controlVirtual inertiaInertial responseSynthetic inertia

A B S T R A C T

Power converter technology partially or fully electrically decouples the wind energy source from the grid whichresults in the decrease of system inertia. However, when those units participate in virtual inertial response theirelectromechanical dynamics become coupled to the grid electromechanical modes. To date, there were nocomprehensive studies on how do different elements and parameters of a wind energy conversion system(WECS) impact its virtual inertial response provision. This is important from the standpoint of understanding theexpected wind farm response during frequency containment process as well as from the standpoint of developingbetter inertial response controllers. In this paper we have investigated how do operating point, line-side andmachine-side converter, phase-locked loop and pitch angle control impact the inertial response of the totalpower controlled type III WECS (DFIG) which is one of the most common wind turbine topologies used today.We show that the operating point, pitch angle control and outer loop of the machine-side converter have a visibleimpact on strength of the inertial response, while other elements do not and some can even be neglected ininertial response studies.

1. Introduction

A high rate of penetration of renewable energy sources (RES) in thelast decade has brought along certain problems for power systems oftoday as well as for power systems of tomorrow. Variable and stochasticRES (of which wind energy and solar photo-voltaic (PV) energy are themost prolific representatives) are connected to the grid via powerelectronic interface which ensures power production at the rated gridfrequency. Connection of this converter-connected generation and de-commissioning of large synchronous units has a couple of con-sequences:

1. grid inertia is reduced since power electronics decouple the rotatingmass from grid frequency (in the case of PVs there is no rotatingmass);

2. traditionally, these sources operate at the maximum power pointand do not ensure a certain amount of upward reserves 1

That is why a lot of attention has been given to developing auxiliarycontrol algorithms for type-III and type-IV wind energy conversionsystems (WECSs) which enable the utilization of their decoupled kinetic

energy to respond to frequency disturbances, usually named virtual orsynthetic inertia [1–8]. Moreover, WECSs can be operated according tosome sub-optimal power curve which ensures a certain amount ofpower reserve during normal operation [9–13,6,14]. Then, droopcontrol can be added to enable the participation of wind turbine gen-erators (WTGs) in primary frequency control (PFC). This is a heavilyresearched topic on which we will spend no more time on and we referthe reader to [15] to read more about frequency support services fromWPPs. Nevertheless, WECSs are complex electromechanical systemsand there were no comprehensive studies on how exactly do differentparameters and the operating point impact the inertial response anddroop control capabilities of a type-III or type-IV WECS. Type-III windturbines are usually called doubly-fed induction generator (DFIG) windturbines and we will use this term onward.

1.1. Literature survey

Kayikçy and Milanović [16] thoroughly investigated the impact ofmodel order of a DFIG-based wind turbine on transient response (short-circuit) and they concluded the following: constant wind power orconstant mechanical torque assumptions are not realistic; simplification

https://doi.org/10.1016/j.epsr.2019.106005Received 9 April 2019; Received in revised form 22 July 2019; Accepted 13 August 2019

⁎ Corresponding author.E-mail addresses: matej.krpan@fer.hr (M. Krpan), igor.kuzle@fer.hr (I. Kuzle).

1 today, most grid codes require that wind power plants have the capability of an upward reserve, but most of them do not require wind farms to continuouslyoperate with that reserve

Electric Power Systems Research 178 (2020) 106005

Available online 17 September 20190378-7796/ © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

T

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of the converter and machine models does not significantly influencethe transient response of the DFIG; DC voltage can be assumed constant.In [17], the same authors analyzed the impacts of the following aspectson system frequency response: control strategy (power or torque),maximum-power-point-tracking (MPPT) characteristic, initial loadingand auxiliary inertial controller parameters. They concluded thattorque control is more stable than power control, MPPT curve providesa self-stabilizing mechanism, initial loading has a significant impact ofinertial response provision due to the converter limits and that variouspower and frequency responses could be obtained depending on thedesign of the inertial controller, but no sensitivity analysis was done. Insome of our recent work [18,19], we have analyzed the small-signalresponse of a total power controlled variable speed wind turbine(VSWT) and we have shown the following: impact of the operatingpoint on the combined VIR and PFC depends on the control structure,more precisely on the power tracking and set-point curve. Weaker re-sponse is generally recorded for higher wind speeds. However, thedesign of the deloaded curve around the maximum rotor speed resultsin a stronger and more oscillatory response which can sometimes beunstable. We have also shown that the inertia of the wind turbinedoesn’t have a significant impact on the grid frequency following adisturbance except in the aforementioned region where bigger windturbines result in deteriorated frequency response. The former is in linewith the well-known decoupling effect of power converters, while thelatter is a consequence of the power set-point algorithm. Pitch angleservomechanism time constant doesn’t have an effect at above rated

wind speeds, while in the region around maximum rotor speed slowerpitch angle control results in a more oscillatory behaviour of the gridfrequency. However, in [18,19], simplified wind turbine model wasused (generator and electrical control were not taken into account). Thegrid was replaced by a simple low-order system frequency responsemodel with turbine dynamics. Recently, research has shown [20,21]that there is a link between the virtual inertial response (VIR) andphase-locked loop (PLL) which can affect both the small-signal stabilityof the power system and the strength of the VIR. Arani and Mohamed[22] analyzed the impacts of droop control in DFIGs on microgrid andweak grid stability and they also concluded that torque control is morestable than power control. They have also shown that pitch anglecontroller does not have a significant impact on droop control, but nostudies on inertial response were done. Quan and Pan [23] analyzed theimpact of operating point of a total power controlled DFIG on si-multaneous provision of inertial response and droop response using themodel linearization and they have concluded the following: power in-jection is stronger under lower wind speeds in the medium wind speedregion (where power is proportional to the cube of the generatorspeed). They did not analyze behaviour under low wind speeds norunder high wind speeds. On the other hand, Hu et al. [24] showed thatthe inertial response of a torque-controlled DFIG is stronger underhigher wind speeds (in the MPPT region). They also showed that thehigher PI gains of the speed controller weaken the inertial response dueto the bigger restraining effect. However, they used a simplified DFIGmodel. Based on the literature survey, a comprehensive study is

Nomenclature

* Superscript denoting a set-point value (reference)d Subscript denoting d-axis valueq Subscript denoting q-axis valueβ Pitch angleγ Shaft twist angleλ Tip-speed ratioρ Air densityωg Electric angular frequency of the generator rotorωs Electric angular frequency of the grid (ωs = 2πfs)ωt Mechanical angular frequency of the turbineCp(λ, β) Wind turbine power coefficientDs Shaft damping constantHg DFIG inertia constantHt Wind turbine inertia constantKp Proportional gain of a PI controllerKi Integral gain of a PI controllerKs Shaft stiffness

Kv Virtual inertia constantR Wind turbine rotor radiusTg Generator electrical torqueTm Turbine mechanical torqueTs Pitch servo time constantvw Wind speedDFIG Doubly fed induction generatorPLL Phase-locked loopMSC Machine-side converter (rotor-side converter)LSC Line-side converter (grid-side converter)MPPT Maximum power-point trackingPWM Pulse-width modulationSG Synchronous generatorRMS Root mean squareVIR Virtual inertial responseROCOF Rate-of-change-of-frequencyWECS Wind energy conversion systemWTG Wind turbine generator

Fig. 1. Test system.

M. Krpan and I. Kuzle Electric Power Systems Research 178 (2020) 106005

2

required to analyze the impact of various parameters on virtual inertialresponse from DFIGs. With that being said, this paper is based uponpreliminary analysis from [25] and it contains much more exhaustiveanalysis.

1.2. Contribution

Based on the literature survey, one can see that there were nocomprehensive studies on the sensitivity analysis of various DFIG ele-ments on inertial response provision. These elements are: machine-sideconverter (MSC) and line-side converter (LSC) controller parameters,PLL parameters, pitch angle controller parameters and initial operatingpoint). The active power response of a DFIG-based wind turbine and theimpact of the aforementioned parameters heavily depend on the type ofthe control design of the WECS. Furthermore, no multidimensionalanalysis was done in any of the surveyed literature from Section 1.1. Inthis paper, we have focused on the total power control as one of thefrequently used schemes in the literature. The main contribution of thispaper is to understand how different elements of a DFIG WECS impact

the provision of inertial response in order to facilitate further researchregarding wind turbine control design as well as to shed light onto thefact that different responses from wind farms may be expected duringfrequency containment process. To the best of our knowledge, this issomething that was not done before. Furthermore, we note that theresponse of the WECS to frequency disturbance differs between dif-ferent types of models in some aspects. This is an important findingbecause using different models can result in arriving to contradictoryconclusions while doing power systems research.

Therefore, the contributions of this paper are as follows:

• analysis of the impact of the DFIG operating point on VIR for thewhole operating regions from cut-in to cut-out;

• multidimensional sensitivity analysis of the impact of the DFIGcontrol system parameters on the dynamic characteristics of theVIR;

• to clarify, illustrate and discuss in detail the characteristics of thetotal power control of DFIG WECS and how it affects the provision ofvirtual inertia;

• finding that inertial response sensitivity to initial conditions de-pends on the type of MPPT control algorithm.

The rest of the paper is organized as follows: In Section 2, the testsystem used for simulations and methodology are presented. In Section3, we analyze and discuss the impact of the aforementioned variableson the VIR provision by the total power controlled DFIG WECS. Section4 concludes the paper.

2. Methodology

Fig. 1 shows the test system used in the simulations. It is a two-machine system consisting of a DFIG-based wind power plant (con-sisting of 15 aggregated 2 MVA turbines) and a 75 MVA synchronousgenerator interconnected through a series of lines and transformers.Wind power penetration is equal to 28.5% of total installed capacity.Loads are connected to bus 6. We understand that this is not the mostrealistic depiction of a power system, but it is the simplest form of asystem for studying frequency dynamics. The synchronous machinerepresents the rest of the bulk power system while isolating the averagefrequency dynamics from other factors such as grid topology,

Fig. 2. wind turbine model and control system.

Fig. 3. Power vs. generator speed curve of the test DFIG.

M. Krpan and I. Kuzle Electric Power Systems Research 178 (2020) 106005

3

interaction between different controllers, different turbine types, etc.which are beyond the scope of this paper. The classical model of thesynchronous machine is used and it is equipped with a TGOV1 turbine-governor model and a IEEET1 automatic voltage regulator (AVR). In alltest cases, a frequency disturbance is induced by connecting the 5 MWload at t = 1 s which is equal to 5% of the total generation capacity and10% of pre-disturbance load. Parameters of the test system are given inthe Appendix. Electromechanical transient simulation (RMS values) isconducted in DIgSILENT PowerFactory 2019 software package.

Fig. 2 shows the overall control system of the DFIG model used inthis paper. MPPT or deloaded operation is set by setting the mode flagto 0 or 1, respectively. Fig. 3 shows the generator power vs. rotor speedcurve for both MPPT and deloaded operation. However, since we arefocusing on VIR, the DFIG will be operating according to the MPPTcurve. Parameters of the complete wind turbine system are given in theAppendix.

Now, we briefly present the mathematical model of the DFIG windturbine used in this paper. Wind turbine mechanical power is calculatedas (1) [26]:

=P v R C v v t( , , ) 12

( , , ) ( ),m t w p t w w2 3 (1)

where the aerodynamic power coefficient Cp is a complex analytic ex-pression and can be found in [27]. Electrical power set-point Pppt(power-point tracking) depends on the operating region of the turbine(Fig. 3) and is described by (2)–(4):

=P P P t· ( ).A B A BB B A A

gB B

gA A gppt

// /

/ /(2)

In the region B − C/B′ − C′ generator power is proportional to thecube of the generator speed and a coefficient kg which can be calculatedusing an iterative method due to the nonlinearity of the aerodynamics[28]:

=P k t( ).B C B C g gppt / 3 (3)

In the region C′ − D′ in deloaded mode, the maximum speed is reachedand the power set-point is obtained from the estimated wind speed[29,30]:

= =P f v( )| .C D wppt const.g (4)

Generator power and speed at points ABCD/A′B′C′D′ are constantcoefficients calculated during the turbine design. At points C and D′power set-point is equal to the nominal and maximum deloaded power,respectively—and the pitch angle controller restricts the turbine speedto the maximum speed. Shaft dynamics are described by the two-massmodel (5):

Fig. 4. Dynamic characteristics of the DFIG inertial response for varying wind speeds.

Fig. 5. Phase-locked loop model.

M. Krpan and I. Kuzle Electric Power Systems Research 178 (2020) 106005

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=

= +

=

H d T K D

Hd

K D T

d f

2dt

( )

2dt

( )

dt2 ( ).

tt

m s s t g

gg

s s t g g

n t g (5)

DFIG model is an existing element in DIgSILENT PowerFactorysoftware modelled in rotor reference frame. It is controlled with themodulation factors P*mq and P*md from the MSC. P*mq and P*md are ex-pressed in the rotor reference frame, however they are initially ob-tained in the stator-flux reference frame in which the MSC operates.

LSC as well as the DC capacitor are additionally considered as well.LSC operates in the stator-voltage reference frame. Both MSC and LSCare modelled with the fundamental frequency model (for RMS studies)of the voltage source converter element with sinusiodal PWM. Theconverter AC voltage Vac is related to the converter DC voltage Vdc by(6):

= +V V P P32 2

( * j * ),ac dc mr mi (6)

where P*mr and P*mr are real and imaginary parts of the modulation index

depending on the reference frame used. All the MSC and LSC PI con-trollers are non-windup to prevent the windup effect of the integralcontroller.

Pitch control is described by (7). Pitch controller is also a non-windup controller. Pitch angle β is limited between 0 and 27° and thepitch rate is limited to ± 10°/s.

= +

=

K K d

T d* ( *) ( *)( )

dt* .

p t i t

s (7)

3. Dynamic characteristics of virtual inertial response

3.1. Impact of initial wind speed

The DFIG is initialized at point B (Fig. 3) and the wind speed islinearly increased from ∼7 m/s to ∼25 m/s. Pitch control becomesactive around 12 m/s. Inertial response is not considered in zone ABbecause of the low speed and the increased possibility of stalling. Im-pact of the initial conditions (initial wind speed) is visible in Fig. 4a–d.Generally, when the inertial response is activated at point B (in this case

Fig. 6. Dynamic characteristics of the DFIG inertial response for different PLL PI controller parameters.

M. Krpan and I. Kuzle Electric Power Systems Research 178 (2020) 106005

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around 6.9 m/s), the generator speed will drop resulting in shifting thepower set-point curve from BC to the line AB. This in turn results inslightly lower peak time, lower peak value and a larger undershoot ofthe power injection.

When the wind speed is high enough, the generator speed will stayin the BC region. Here, the peak value of the inertial response fallslinearly with the wind speed while there is no significant impact on thetime when the peak value is reached. The explanation can be found inthe small-signal stability model of the simplified one-mass wind turbinesystem which has been derived in [18,23]; transfer function G(s) whichrelates the power set-point P* to the virtual inertia power output δP is(8) [18,19]:

= =+

+G s P

P

k

k( ) *

2Hs ( | )

2Hs 2 |.

gT

g oT

0 0

0

mg

mg (8)

The gain of this transfer function falls with the increasing initial gen-erator speed (i.e. wind speed) which has been illustrated in Fig. 4d.

Once the pitch control becomes active and the power reference andgenerator speed are controlled to be constant, there is a step increase in

the peak value compared to the previous wind speed step when pitchcontrol was inactive. Then, the peak value of the inertial response fallsnon-linearly with the respect to the increasing wind speed reflecting thenonlinear nature of the pitch angle in the aerodynamic model. Slowerpitch control action is reflected in the peak time compared to when onlyrotor speed control is utilized: peak time jumps from 1.9 s to around2.05 s and falls of with increasing wind speed. This falloff can be at-tributed to the high nonlinearity of the aerodynamic part and theshortcomings of the analytical Cp curve at higher wind speeds [16]. Thepeak value of the inertial response can vary between 0.045 p.u. and0.040 p.u. depending on the wind speed.

On the other hand, Hu et al. [24] used speed-controlled DFIG modelwith inverse MPPT characteristic (rotor controller controls the speedrather than power) and they report stronger inertial response at higherwind speed which brings us to the first conclusion: inertial responsesensitivity is not the same for total power controlled DFIG and for thespeed-controlled DFIG. Value of the virtual inertia constant should bedynamically changed as the function of the generator speed in order toachieve better inertial response and to achieve a consistent power in-jection with respect to both the pre-disturbance power output and therated power.

Fig. 7. Modal analysis of the relevant system modes for different PLL PI controller parameters.

M. Krpan and I. Kuzle Electric Power Systems Research 178 (2020) 106005

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3.2. Impact of PLL parameters

Frequency signal which is used as an input to the virtual inertiacontroller is estimated using a PLL (Fig. 5) which measures the statorvoltage at Bus 1. In the stator flux reference frame, the d-axis coincideswith the stator flux vector and the q-axis coincides with stator voltagevector, and it is 90∘ ahead of the d-axis. The PLL controls the angle θsuch that the d-axis component of the stator voltage is zeroed. In thiscase, θ is the angle of the stator voltage vector relative to the voltageangle at the reference bus (0∘). Inputs to the PLL are the real andimaginary components of the stator voltage in the global (positive-se-quence, xy) reference frame. Estimated grid frequency is equal tofs = ωs/2π. The PLL model is described with (9):

= +

=

( )f K v t K v df d

12

( ) ( )

2 ( ) .

s p ds

i ds

s

PLL PLL

(9)

We vary KpPLL and KiPLL linearly between 1 and 35, and 20 and 35,respectively. Fig. 6 shows the dynamic characteristics of the inertialresponse for different PI parameters for a below rated and an aboverated wind speed. The simulations have shown a few things: firstly, ifKpPLL and KiPLL are large enough, they do not have a significant impacton the strength of the inertial response (Fig. 6a and c). However, forcertain combinations of KpPLL and KiPLL where one or both of those gainsare small, the peak is significantly higher (Fig. 6b and d) than it is for

larger gains, but the complete behaviour is more oscillatory and un-desirable. Smaller PI gains resulted in worse tracking and stronger os-cillations.

Secondly, For smaller PI gains, the DFIG model exhibits a behavioursimilar to a non-minimal phase shift system which is visible through theinitial undershoot in Fig. 6b and d: in the initial moments following adisturbance, the DFIG output power is momentarily reduced furtheraggravating the grid frequency dynamics which in turn results in astronger response. Worse stator voltage angle tracking will indirectlyinfluence the DFIG dynamics because this angle is used for transformingbetween rotor reference frame and stator flux reference frame in therotor-side control system. Furthermore, with smaller PI gains thedamped frequency of the PLL mode is close to that of the electro-mechanical modes of the system which means that the PLL with par-ticipate in the electromechanical oscillations of the system. However,PLL gains are typically large and the PLL mode is well damped [31].

To the contrary, Ma et al. [20] report weaker inertial response undersmaller PLL PI gains and well-damped behaviour. In their paper, theyhave investigated the impact of PLL dynamics on inter-area oscillationsbetween two systems connected with a weak tie-line. We did not noticeany such behaviour in our test system, even with increasing both linelengths from 10 km to 110 km. There can be multiple reasons for thisdiscrepancy between the two results: grid topology, types of excitationsystems and power system stabilizers, controllers parameters, windturbine generator model, etc. This is a complex issue which needs

Fig. 8. Dynamic characteristics of the DFIG inertial response for different MSC outer PI controller parameters.

M. Krpan and I. Kuzle Electric Power Systems Research 178 (2020) 106005

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separate and in depth studies which are beyond the scope of this paper.This behaviour is independent of whether or not the virtual inertial

response is active or not and it mostly depends on the PLL itself. Theparticipation of PLL in electromechanical oscillations is visible byplotting the trajectories of the PLL mode and the system electro-mechanical mode (Fig. 7). PLL mode is related to the PLL state variablesxPLL and . Synchronous generator (SG) mode has a frequency ofaround 1.5 Hz and can be considered a local mode. Fig. 7a shows thatthe parameters of the PLL PI controller do not have a significant impacton the SG mode. On the other hand, PLL mode is close to the imaginaryaxis for small KpPLL values (weak damping) and this oscillatory beha-viour will dominate the response as seen from Fig. 6b and d. By in-creasing the proportional gain of the PLL, damping of this mode is in-creased and at certain point PLL mode ceases to be oscillatory (it iscompletely damped). Fig. 7c shows that the participation factor of PLLstate variables in the SG mode increases for larger KpPLL gain, but doesnot depend on the virtual inertia coefficient.

3.3. Impact of MSC control loops

Machine side converter control system usually consists of a slowerouter loop which generates the q and d axis rotor current references anda faster inner loop which generates the q and d axis rotor voltage re-ferences or similar PWM control signals (in this case, they are q and daxis modulation factors which is one possible option in DIgSILENTPowerFactory). MSC is operated in a stator-flux reference frame whereq axis corresponds to the active power control and d axis corresponds to

the reactive power control. Since the reactive power control is not atopic of this research, only the q axis parameters will be studied.

We mentioned that the outer loop is slower and the inner loop isfaster. Parameter tuning of a PID controller is not a straightforwardprocess and depends on the desired performance as well as on themodel of the system and the type of control (power, torque or speedcontrol [32,24,20]). Nevertheless, Hansen et al. report that betterperformance can be achieved with stronger integral gain. Therefore, wewill approach the analysis of the impact of MSC control loops para-meters on virtual inertial response by considering both weaker andstronger PI action.

3.3.1. Outer loopKpouter and Kiouter are linearly varied between 1.5 and 5, and 0.5 and

8, respectively. Fig. 8 shows the impact of MSC outer PI controller onthe strength of the inertial response. For smaller PI gains the virtualinertial response is stronger (higher apex) for both below rated andabove rated wind speed (Fig. 8a and d). This is because the strongeraction of the outer PI loop restrains the change of the generator powermore [24]. This in turn results in weaker power injection from DFIG.However, if the outer control loop is fast enough (large PI gains) thanthere is no impact on the strength of the inertial response as shown bythe blue shaded areas in Fig. 8a and d. Furthermore, weaker PI gainswill also results in faster peak time as shown in Fig. 8b and e. In timedomain, this is illustrated with two responses for some characteristicstrong and weak combinations of PI gains (Fig. 8c and f). In summary,this means that the dynamics of the slower outer loop should be taken

Fig. 9. Dynamic characteristics of the DFIG inertial response for different MSC inner PI controller parameters.

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into account when studying inertial response dynamics. They can onlybe neglected if the PI gains are large such that the whole loop has fasterset-point tracking.

3.3.2. Inner loopKpinner and Kiinner are linearly varied between 0.1 and 1.4, and 10 and

100, respectively. Impact of the much faster inner loop dynamics isnegligible as shown in Fig. 9. Impact on the strength of the inertialresponse is in the order of 10−4 (Fig. 9a) and the impact on the peaktime is in the order of 10−2 (Fig. 9b). Inertial response peak time sur-face plot has some random fluctuations that exist due to the interactionof certain combinations of PI parameters that may influence the be-haviour of the model and the numerical integration (i.e. smaller pro-portional and/or integral gains). Compared to the below rated windspeed scenario when the pitch angle control is not active (Fig. 9a),strength of the inertial response is much more sensitive to >K 1pinner(Fig. 9d) for about an order of the magnitude (10−3). The only visibleimpact is in the initial fast transient behaviour as shown in Fig. 9c.Therefore, the dynamics of the inner loop can be neglected in DFIGinertial dynamics and they don’t have an influence on the inertial re-sponse.

3.4. Impact of pitch control

Pitch control is active only at above rated wind speeds to keep the

rotor from over-speeding. There are four main parameters which wehave studied to see how they impact the DFIG inertial response: pro-portional and integral gain of the PI controller (Kppitch and Kipitch, re-spectively) that generates the pitch servo reference β*, time constant ofthe pitch servo mechanism Ts and the pitch rate limit.

3.4.1. PI controllerKppitch and Kipitch are varied between 80 and 300, and 0 and 30, re-

spectively. Stronger inertial response is achieved with larger Kppitch

while the Kipitch doesn’t have a significant influence on the strength ofthe inertial response (Fig. 10a). Time at which the peak of the activepower injection occurs is longer for bigger Kppitch while the Kipitch doesn’thave a significant contribution (Fig. 10b). Fig. 10c shows two DFIGinertial responses for a couple of characteristic combinations of thepitch PI controller. We can conclude that the pitch PI controller para-meters should be taken into account when studying virtual inertialdynamics during above rated wind speeds

3.4.2. Pitch servomechanism time constant and rate limiterGenerally, peak value of the inertial response decreases (Fig. 11a)

and the peak time of the inertial response increases (Fig. 11b) for in-creasing the pitch servo time constant. However, this sensitivity is notsignificant: peak value changes are in the order of 10−4 and peak timechanges are in the order of 10−2. Therefore, pitch servo time constantfor some characteristic values does not have a significant impact on the

Fig. 10. Dynamic characteristics of the DFIG inertial response for different pitch PI controller parameters.

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DFIG inertial response (Fig. 11c). Pitch rate limit has been changedfrom ± 3°/s to ± 13°/s and it also does not influence the dynamics ofthe inertial response (Fig. 11d).

3.5. Impact of LSC and DC capacitor

Line-side converter keeps the DC capacitor voltage constant andcontrols the power factor of the LSC. Inner current control loops will bedisregarded in this section since they are fast and do not influence theinertial response as shown in section 3.3.2. Varying the GSC DC loopparameters does not influence the inertial response of DFIG, as can beseen in Fig. 12a–d. Furthermore, the capacitance of the DC link capa-citor does not impact the inertial response dynamics (Fig. 12e). Gen-erally, LSC and DC link dynamics can be neglected in inertial responsestudies.

4. Conclusion

In this paper we have thoroughly investigated the sensitivity ofvirtual inertial response to various parameters of the WECS usingmultidimensional analysis. These parameters are: initial operatingpoint, machine-side and line-side converter controller parameters, pitchangle control parameters and PLL parameters. The conclusions arelisted below.

Impact of the wind speed on the strength of the inertial responsedepends on the type of machine-side converter control. For total powercontrolled WECS, the response is weaker with increasing wind speed,while for the speed control with inverse MPPT characteristic the re-sponse is stronger with increasing wind speed. Once the pitch controlbecomes active, the peak is initially slightly higher than the instancebefore pitch angle control activation. Then, the response also becomes

weaker with increasing wind speed. Near the cut-in speed, inertial re-sponse will reduce the generator speed which will result in shiftingfrom the MPPT curve to the quasi-constant rotor speed line. This, inturn, results in a lower peak value and peak time. The gradient of thepower vs. rotor speed curve in this region has an impact on the dy-namics, but detailed analysis of this region was out of the scope of thispaper.

Small values of PLL PI gains will result in in more oscillatory be-haviour and weak damping of the local mode. Following a disturbance,the DFIG power is momentarily reduced further aggravating the gridfrequency although the actual peak value is higher. On the other hand,large gains result in strong tracking, no oscillations and smaller peakvalue of the inertial response. Generally, PLL dynamics can be ne-glected if the PLL is fast and the modes are well-damped.

Outer control loop of MSC has an impact on virtual inertial responseprovision. If the outer loop ihas smaller PI gains, the inertial response isstronger and peak time is shorter. This is because it will take a longertime for the weaker controller to restrain the power changes towardsthe set-point.

Inner loop of the MSC control, DC voltage loop and the inner loop ofthe LSC and the DC capacitor dynamics can be neglected in the inertialresponse studies since they are very fast.

Between all the parameters of the pitch control subsystem, pro-portional gain of the PI controller has the most significant impact on theinertial response. Larger proportional gain will results in bigger poweroutput. Inertial response is not significantly sensitive to integral gainnor to the pitch servo time constant.

Future research may include: comparative analysis between dif-ferent DFIG-based wind turbine models and control structures, virtualinertia dynamics of full converter WECS with different control struc-tures and droop dynamics of DFIG/full-converter wind turbines.

Fig. 11. Dynamic characteristics of the DFIG inertial response for different pitch servo time constant Ts.

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[Test system parameters]

Wind turbine and shaft parameters: nominal/base power: 2 MVA;rotor radius: 37.5 m; gearbox ratio: 87; nominal wind speed: 12 m/s;turbine inertia constant: 4.33 s; shaft-stiffness: 0.46 p.u./el. rad.; shaft-damping: 0 p.u.

DFIG parameters: stator voltage: 690 V (line-to-line, RMS); ratedapparent power: 2.28 MVA; frequency: 50 Hz; number of pole-pairs: 2;stator resistance/reactance: 0.01/0.1 p.u.; rotor resistance/reactance(referred to stator): 0.01/0.1 p.u.; magnetizing reactance: 3.5 p.u.; in-ertia constant: 0.6 s; DC capacitor: 10 mF.

RSC parameters: outer control loop: Kp = 4, Ki = 10; inner controlloop: Kp = 1, Ki = 100.

GSC parameters: apparent power: 0.8 MVA; rated AC voltage:0.69kV; rated DC voltage: 1.5 kV; DC voltage control loop: Kp = 8, Ki = 40;inner control loop: Kp = 1, Ki = 100.

Line-side filter: apparent power: 2 MVA; short-circuit voltage: 10%.PLL parameters: Kp = 50, Ki = 150.Pitch angle controller parameters: Kp = 150, Ki = 25; servo-

mechanism time constant: 0.3 s; max. rate-of-change-of-pitch: ± 10°/s.Auxilliary frequency controller parameters: =K 10v ; = 1v s; = 1w ;

Kd = 0.Synchronous generator parameters: Apparent power: 75 MVA; nom-

inal voltage: 20 kV (line-to-line, RMS); Inertia constant: 3 s; stator re-sistance/reactance: 0.05/0.1 p.u.; synchronous reactance xd/xq: 1.5/1.5p.u.; transient reactance x x/d q: 0.256/0.3 p.u.

AVR parameters (IEEET1): default parameters in DIgSILENTPowerFactory.

Turbine-governor (TGOV1) parameters: high-pressure fraction FH: 0.3,reheat time constant Tr: 8 s; droop: 5 %; governor time constant Tg: 0.3s.

0.69/20 kV transformer parameters: nominal power: 100 MVA; short-circuit voltage: 10%; copper losses: 500 kW.

20/220 kV transformer parameters: nominal power: 3 MVA; LV/HVvoltage ratio: 0.69/20 kV; short-circuit voltage: 10%; copper losses: 30kW.

Overhead line parameters: rated voltage: 220 kV; rated current: 0.4kA; resistance: 0.05 Ω/km; reactance: 0.488 Ω/km; length: 10 km.

Acknowledgements

The work of the authors is a part of the H2020 project CROSSBOW –CROSS BOrder management of variable renewable energies and storageunits enabling a transnational Wholesale market (Grant No. 773430).This document has been produced with the financial assistance of theEuropean Union. The contents of this document are the sole responsi-bility of authors and can under no circumstances be regarded as re-flecting the position of the European Union. This work has been sup-ported in part by the Croatian Science Foundation under the projectWINDLIPS –WIND energy integration in Low Inertia Power System(grant No. HRZZ-PAR-02-2017-03).

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Dynamic characteristics of virtual inertial response provision by DFIG-based wind turbinesIntroductionLiterature surveyContribution

MethodologyDynamic characteristics of virtual inertial responseImpact of initial wind speedImpact of PLL parametersImpact of MSC control loopsOuter loopInner loop

Impact of pitch controlPI controllerPitch servomechanism time constant and rate limiter

Impact of LSC and DC capacitor

Conclusion[Test system parameters]AcknowledgementsReferences